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Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies.In this paper,it is shown that an inequality relating to L_p-version of the Petty's conjectured projection inequality is developed by using the notions of the L_p-mixed volume and the L_p-dual mixed volume,the relation of the L_p-projection body and the geometric bodyΓ_(-p)K,the Bourgain-Milman inequality and the L_p-Busemann- Petty inequality.In addition,for each origin-symmetric convex body,by applying the Jeusen inequality and the monotonicity of the geometric bodyΓ_(-p)K,the reverses of L_p-version of the Perry's conjectured projection inequality and the L_p-Petty projection inequality are given,respectively. 相似文献
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联系投影不等式Petty猜想的Lp-形式的不等式 总被引：1，自引：0，他引：1
在凸体理论中,投影不等式的Petty猜想是一个著名的公开问题.首先通过利用Lp-混合体积和Lp-对偶混合体积的概念、Lp-投影体和几何体Γ_pK的关系、Bourgain-Milman不等式和Lp-Busemann-Petty不等式,建立了一个联系投影不等式Petty猜想的Lp-形式的不等式.继而对于每一个关于原点对称的凸体,应用Jensen不等式和几何体Γ_pK的单调性,分别给出了投影不等式Petty猜想的Lp-形式的一个逆向不等式和Lp-Petty投影不等式的一个逆向不等式. 相似文献
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